The Annals of Probability

Stochastic calculus for symmetric Markov processes

Z.-Q. Chen, P. J. Fitzsimmons, K. Kuwae, and T.-S. Zhang

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Abstract

Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an Itô formula for Dirichlet processes is obtained.

Article information

Source
Ann. Probab., Volume 36, Number 3 (2008), 931-970.

Dates
First available in Project Euclid: 9 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.aop/1207749086

Digital Object Identifier
doi:10.1214/07-AOP347

Mathematical Reviews number (MathSciNet)
MR2408579

Zentralblatt MATH identifier
1142.31005

Subjects
Primary: 31C25: Dirichlet spaces
Secondary: 60J57: Multiplicative functionals 60J55: Local time and additive functionals 60H05: Stochastic integrals

Keywords
Symmetric Markov process time reversal stochastic integral generalized Itô formula additive functional martingale additive functional dual additive functional Revuz measure dual predictable projection

Citation

Chen, Z.-Q.; Fitzsimmons, P. J.; Kuwae, K.; Zhang, T.-S. Stochastic calculus for symmetric Markov processes. Ann. Probab. 36 (2008), no. 3, 931--970. doi:10.1214/07-AOP347. https://projecteuclid.org/euclid.aop/1207749086


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References

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